HAM Radio 1/HamRadio.cdr/math/linelo/ll.doc

Text File | 1988-08-30 | 9.9 KB | 329 lines

                       COMPUTER PROGRAM LINELOSS



     The program LINELOSS is a versatile program capable of doing

a   variety   of  calculations  related  to  power,   VSWR,   and

transmission  line  losses.   The  program,  and  the   following

explanatory  and  tutorial  information, is  excerpted  from  The

Meteor Burst Communications Handbook, by Jacob Z. Schanker.  This

handbook  was  prepared  under  U.S. Air  Force  Funding.  It  is

expected  that it will be available through the N.T.I.S. late  in

1988.


TRANSMISSION LINES



Losses  in  coaxial  transmission lines can  have  a  significant

effect on system performance. The losses negatively affect system

performance  in  several  ways.  Therefore,  reducing  coax  loss

provides multiple benefits. In fact, reducing coax loss is one of

the easiest, and least expensive, ways to improve  communications

system performance. These are the factors involved:


       1)  Loss in the transmission line between transmitter  and

       the  antenna  reduce the power delivered to  the  antenna,

       thus reducing the effective radiated power.

       2) Loss in the transmission line between receiving antenna

       and  receiver increase the effective noise figure  of  the

       receiver, reducing receiver sensitivity.

       3)  Any  standing  waves on  the  transmission  line  will

       increase  the  losses  on the line. That  is,  the  actual

       transmission line loss will be higher than the rated  line

       loss.  This point is of particular significance  since  it

       further  aggravates the negative effects of the first  two

       factors.


     It's  easy  to understand how line loss  reduces  the  power

delivered  at the end of a transmission line, but the  effect  of

standing waves in increasing the loss requires some  explanation.

Whenever  the  load  at the end of a  transmission  line  is  not

perfectly  matched  to the line, that is when ZL  is  not  purely

resistive and equal in magnitude to the characteristic  impedance

of  the  line  Zo,  standing  waves  will  exist.  The  impedance

inequality at the load will cause power to be reflected back down

the  transmission  line towards the source. This  reflected  wave

undergoes  the  same  amount of attenuation  (in  dB.)  that  the

forward  wave  experienced intitially in travelling  towards  the

load.   This   attenuation   increases   the   overall,   actual,

attenuation. The actual attenuation is always greater than the

rated  line  attenuation, except when a  line  is  perfectly

"flat" (no standing waves).



     The  load in a communications system is either the  antenna,

or  the  receiver  input. In either case, it is  unlikely  to  be

perfectly  matched  to the line, which will normally  be  coaxial

cable with     50 ohm nominal characteristic impedance. A  multi-

element  Yagi  beam antenna carefully tuned to the  frequency  of

operation  may  have a relatively low VSWR, typically  less  than

1.5,  and possible as low as 1.1. On the other hand,  a  wideband

log-periodic  beam antenna may have a VSWR above 2.0.  The  input

impedance  of a typical receiver is only nominally 50  ohms.  The

actual impedance will vary quite a bit from the nominal, and  the

VSWR is often between 1.5 and 2.0.



     The   rated  attenuation  for  coaxial  cable  is   normally

expressed in terms of dB. per 100 feet or dB. per 100 meters. The

attenuation  is  a  function of frequency of  operation,  so  the

rating  must  specify the frequency at which the  attenuation  is

given.  Manufacturer's  literature, handbooks, or MIL  specs  are

possible sources of this information. Often the rated attenuation

will be given at 10 MHz. and at 100 MHz. Unfortunately, important

communications frequencies lie between these two frequencies, and

attenuation ratings are unlikely to be specified at the  specific

frequencies of operation.  Since the attenuation of coaxial cable

varies  approximately as the square-root of the frequency  ratio,

it is possible to make a useful estimate of rated attenuation  at

specific   frequencies  from  the  rated  attenuation  at   other

frequencies.


     Module  7  of  the MBC Programs, LINELOSS, may  be  used  to

calculate  the rated line loss at a particular  frequency,  given

rated line loss at some other frequency. Once the rated line loss

is  known,  the actual line loss can be calculated  for  whatever

value of VSWR exists on the line. The program also expresses true

line   loss  as  an  operating  efficiency   figure.   Additional

calculations provided in LINELOSS are conversion between  forward

and reflected power and VSWR.


     It's  useful  to plug some numbers into  LINELOSS  and  play

around a bit. The importance of low transmission line loss should

soon  be apparent. Low VSWR is also helpful, but often is not  as

easily   controllable.  As  an  example  of  the   considerations

discussed  above,  and of the use of the  program,  consider  the

following:



     A  meteor burst system operates at 40 MHz. The  remote  site

operates   in   half-duplex  with  the  meteor   burst   terminal

(transmitter/receiver)  connected  to a 5  element  Yagi  antenna

through  150 feet of RG8A/U type coaxial cable. The VSWR  of  the

antenna is 1.30. Use Module 7 to find the true loss in the  line,

the  line  operating  efficiency, and the apparent  VSWR  at  the

terminal end of the line.


     The  rated attenuation of RG8A/U, from manufacturer's  data,

is  0.56 dB. per 100 feet at 10 MHz. From the Main  Menu,  choose

selection  2, "FIND RATED LINE LOSS AT OPERATING  FREQUENCY  FROM

RATED VALUE AT ANOTHER FREQUENCY." The rated line loss, 0.56  dB.

is  entered  first. The actual line length, 150  (feet)  is  then

entered  in response to the prompt. Next, the frequency at  which

the  rating  was  given, 10 (MHz.) is entered,  followed  by  the

actual  operating  frequency  of  40  (MHz.).  The  program  then

calculates  the rated attenuation for 150 feet at 40  MHz.  using

the approximation that attenuation is proportional to the  square

root  of  the actual frequency divided by the  rating  frequency.

This  is accurate enough for most purposes. Note that  the  value

obtained from the program is 1.7 dB. Choose selection 2 to return

to the Main Menu, we then choose selection 4 "CALCULATIONS, USING

CONDITIONS AT ANTENNA END", since we know the VSWR at the antenna

end. The rated line loss for the length of line being used, which

we  just found to be 1.7 dB. is entered first. The  program  then

asks us to enter any additional losses in the transmission  path.

These  could be due to filters, diplexers, or  other  accessories

which exhibit some insertion loss. In this case, we assume  there

is no additional loss and so enter 0. Finally, we enter the known

VSWR at the antenna, 1.3, in response to the prompt.



     The program then calculates that the VSWR at the transmitter

end  is  1.19.  This  points  up  the  fact  that  for  a   lossy

transmission line, the VSWR at the transmitter (source) end  will

always be less than the VSWR at the antenna (load) end. This is a

result  of:  (1) the forward power delivered to  the  antenna  is

reduced by the line attenuation, and, (2) the resulting reflected

power caused by the antenna mismatch is further attenuated on its

return trip to the transmitter end. Since VSWR is proportional to

the  ratio of reflected power/forward power, the transmitter  end

sees a lower reflected power and a higher forward power than  the

antenna end, hence a lower VSWR.



     Then  program the calculates that the true overall  loss  in

the  line  (accounting for the effect of VSWR on the  rated  line

loss)  is  1.74  dB.,  and that  the  overall  transmission  line

operating  efficiency is 67.0%. Note that, in this  example,  the

VSWR  on  the line contributed negligible  (.04  dB.)  additional

loss.  Since  the VSWR was relatively low (1.3) this is  not  too

surprising. But what if the antenna VSWR was 2.5? This is a value

which  might be seen with a log-periodic type antenna, or with  a

field  expedient  antenna.  It is suggested that  the  reader  go

through  the calculations for this case. The result is  that  the

true line loss is 2.20 dB., an increase of 0.5 dB. over the rated

line loss which would be exhibited for unity VSWR.



     As another example, consider that in the previous example we

did  not  know  the VSWR of the antenna. However,  using  a  BIRD

wattmeter  or  similar  instrument,  the  forward  power  at  the

transmitter  end  was measured as 300 watts,  and  the  reflected

power  as  20  watts. This may seem pretty good,  but  it  isn't.

Choose  selection 1 "CONVERT BETWEEN VSWR AND  REFLECTED  POWER",

from the Main Menu. Entering our values, we find that the VSWR is

1.70.  Returning  to  the  Main Menu  and  choosing  selection  3

"CALCULATIONS, USING CONDITIONS AT TRANSMITTER END", the  program

calculates  that  the true VSWR at the antenna end is  2.24,  and

that  the true overall loss is 2.09 dB. This is 0.39  dB  greater

loss than the rated line loss of 1.7 dB. The calculated operating

efficiency  is 61.8%. This means that the actual power  delivered

to  the  antenna  to  be radiated is 0.618  X  (Forward  Power  -

Reflected Power) or   0.618 X (300 - 20) = 173 watts.


Additional reference:


"Program Finds True Transmission Line Loss" EDN, February 18, 1981